LONDON, Sept 7 (Reuters) - Italy’s borrowing costs fell to one-month lows on Friday, setting the bond market up for its best week since June thanks to an easing of concerns about possible fiscal largesse from the new anti-establishment government.

Short-dated Italian bond yields have fallen around 57 basis points this week after reassuring comments from senior members of the government suggested that Rome will respect European Union rules on fiscal discipline.

Italy’s treasury bought back 2.75 billion euros over four bonds on Friday in a reverse auction aimed at reducing its public debt.

The buy-back, announced on Wednesday, adds to similar deals in recent weeks that have helped stabilise a bond market battered by concerns about the new government’s spending plans.

“When they announced this buyback there was also a positive turnaround in investor sentiment related to constructive budget talks, so there is a combined boost to the bond market,” said UniCredit bond strategist Luca Cazzulani.

“Whether the positive market tone continues depends on the statements and tone in the budget discussions; this is the most important thing.”

Italy’s 10-year bond yield fell 9 basis points (bps) to 2.81 percent, its lowest in a month, before settling at 2.87 percent. It has fallen 36 bps this week, its biggest weekly fall since June and one of its biggest weekly drops since the euro zone debt crisis.

That has left the closely watched gap over top-rated German Bund yields at about 249 bps, close to its tightest in a month.

Italian two and five-year bond yields were also set for their biggest weekly falls since June.

The recovery in Italian debt has dented the appeal of safe-haven German bonds, with short-dated Bund yields up about 6 bps this week at minus 0.56 percent and set for their biggest one-week rise since February.

Analysts say the rally in Italian debt prices also represents some covering of bearish positioning and a relentless hunt for higher-yielding assets from investors.

Rabobank analysts said a report in Italy’s La Repubblica that finance minister Tria is aiming to keep the budget deficit below 1.6 percent may also have helped bond market sentiment.

Most bond yields in the euro area rose on Friday, leaving Italy as the clear outperformer, after stronger than expected employment data and wage growth in the United States pushed U.S. Treasury yields sharply higher.

German 10-year yields, the benchmark for the bloc, were up nearly four basis points on the day at 0.386 percent.